Finite Math Examples

14

$14$ ,

17

$17$ ,

71

$71$ ,

74

$74$ ,

11

$11$ ,

44

$44$ ,

77

$77$ ,

47

$47$ ,

41

$41$ ,

17

$17$ ,

14

$14$

Step 1

The five-number summary is a descriptive statistic that provides information about a set of observations. It consists of the following statistics:

1. Minimum (Min) - the smallest observation

2. Maximum (Max) - the largest observation

3. Median

M

$M$ - the middle term

4. First Quartile

Q_{1}

$Q_{1}$ - the middle term of values below the median

5. Third Quartile

Q_{3}

$Q_{3}$ - the middle term of values above the median

Step 2

Arrange the terms in ascending order.

11, 14, 14, 17, 17, 41, 44, 47, 71, 74, 77

$11, 14, 14, 17, 17, 41, 44, 47, 71, 74, 77$

Step 3

The minimum value is the smallest value in the arranged data set.

11

$11$

Step 4

The maximum value is the largest value in the arranged data set.

77

$77$

Step 5

The median is the middle term in the arranged data set.

41

$41$

Step 6

Find the first quartile by finding the median of the set of values to the left of the median.

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Step 6.1

The lower half of data is the set below the median.

11, 14, 14, 17, 17

$11, 14, 14, 17, 17$

Step 6.2

The median is the middle term in the arranged data set.

14

$14$

14

$14$

Step 7

Find the third quartile by finding the median of the set of values to the right of the median.

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Step 7.1

The upper half of data is the set above the median.

44, 47, 71, 74, 77

$44, 47, 71, 74, 77$

Step 7.2

The median is the middle term in the arranged data set.

71

$71$

71

$71$

Step 8

The five most important sample values are sample minimum, sample maximum, median, lower quartile, and upper quartile.

Min = 11

$Min = 11$

Max = 77

$Max = 77$

M = 41

$M = 41$

Q_{1} = 14

$Q_{1} = 14$

Q_{3} = 71

$Q_{3} = 71$

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